The HA community is truly impressive! Thank you all for your very interesting replies to my newbie question. I have spent the last days reflecting on them and thinking about my way forward.
I understand now that « input numbers » have their own state, and thus survive restarts.
This is not the case for template numbers, unless you « hardwire » the value into the state field 
This is what I have doing for various constants associated with my shutters (pre-set positions, and compass orientations). To allow these constants to be set by the end user, I would to have use input numbers. But then I would lose the convenience (for me) of « linking » these constants to the shutter devices (so that they appear in « device info »). I suppose that I could group them all together in a dashboard « shutter » card, which would have the same effect. That’s probably what I’ll do if I go for user-settable constants.
I amused myself by creating an « input number » + « template number » pair, where the initial state of the template number is obtained from the input number, and where an action « on set value » is defined that writes back the modified value to the input number. A bit cumbersome but it works!
I don’t know what is the correct procedure for requesting features, but two features that would seem really useful (to me) are:
- The possibility to link an input number to a device (so that it appears in device info).
- The possibility to display template numbers as simple numeric fields, without a movable slider or up-down increment arrows.
Regarding (2) above, I would be interested to see other use cases of the up-down increment arrows (or slider) on a template number. I found the examples at Template - Home Assistant rather contrived. Until now, I have been using template numbers as either constants or calculated « variables », much like template sensors.
Finally, I should point out that since I am using Home Assistant Green then, as far as I understand, all entity definitions must be carried out via the UI, which in the case of template numbers, requires a definition of state, and does not have any notion of « optimistic ».
Again, thanks to all.